Following a discussion of the statue of our cognition and descriptions in publicly observable physical material reality, and of our internal states, such as our thoughts, emotions and feelings of pain, it is argued that conditions exist which apply equally for the inter-subjectivity of cognition and description of both publicly observable thing and internal states. It is shown that on these conditions rests the possibility of persons together developing criteria or standards for determining and distinguishing between what is and what is not publicly observable. The same conditions, so it is argued, rule out any consistent notions of private cognition and languages. On these conditions, furthermore, relies the possibility of persons talking about their individual differences – concerning both what is and what is not publicly observable – and thus for a person to be a person different from other persons. The paper concludes by outlining the consequences for constructivists and traditional Cartesian assumptions on the acquisition and development of cognition and language which underly present day Cognitive Science.